Many problems in scientific computing involving a large sparse matrix A are solved by Krylov subspace methods. This includes methods for the solution of large linear systems of equations with A, for the computation of a few eigenvalues and associated eigenvectors of A, and for the approximation of nonlinear matrix functions of A. When the matrix A is non-Hermitian, the Arnoldi process commonly ...

Abstract Our aim in this paper is presenting an attractive numerical approach giving accurate solution to the nonlinear fractional Abel differential equation based on a reproducing kernel algorithm with model endowed Caputo–Fabrizio derivative. By means of such approach, we utilize Gram–Schmidt orthogonalization process create orthonormal set bases that leads appropriate Hilbert space $\mathcal...

In conventional hybrid beamforming approaches, the number of radio-frequency (RF) chains is bottleneck on achievable spatial multiplexing gain. Recent studies have overcome this limitation by increasing update-rate RF beamformer. This paper presents a framework to design and evaluate such which we refer as agile beamforming, from theoretical practical points view. context, consider impact RF-ch...

This paper is concerned with a technique for solving Volterra integral equations in the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernel method, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series.An iterative method is given to obtain the approximate solution.The conver...

This paper is concerned with a technique for solving Volterra integro-dierential equationsin the reproducing kernel Hilbert space. In contrast with the conventional reproducing kernelmethod, the Gram-Schmidt process is omitted here and satisfactory results are obtained.The analytical solution is represented in the form of series. An iterative method is given toobtain the...

A novel significant vector (SV) regression algorithm is proposed in this paper based on an analysis of Chen's orthogonal least squares (OLS) regression algorithm. The proposed regularized SV algorithm finds the significant vectors in a successive greedy process in which, compared to the classical OLS algorithm, the orthogonalization has been removed from the algorithm. The performance of the pr...

The nonlinear integral equation P (x) = ∫ β α dy w(y)P (y)P (x + y) is investigated. It is shown that for a given function w(x) the equation admits an infinite set of polynomial solutions P (x). For polynomial solutions, this nonlinear integral equation reduces to a finite set of coupled linear algebraic equations for the coefficients of the polynomials. Interestingly, the set of polynomial sol...